Find the Discriminant 4x^2-45x-269=7x^2-3x+7

$4 x^{2} - 45 x - 269 = 7 x^{2} - 3 x + 7$

Move all terms to the left side of the equation and simplify.

Move all the expressions to the left side of the equation.

Subtract $7 x^{2}$ from both sides of the equation.

$4 x^{2} - 45 x - 269 - 7 x^{2} = - 3 x + 7$

Add $3 x$ to both sides of the equation.

$4 x^{2} - 45 x - 269 - 7 x^{2} + 3 x = 7$

Subtract $7$ from both sides of the equation.

$4 x^{2} - 45 x - 269 - 7 x^{2} + 3 x - 7 = 0$

Simplify $4 x^{2} - 45 x - 269 - 7 x^{2} + 3 x - 7$ .

Subtract $7 x^{2}$ from $4 x^{2}$ .

$- 3 x^{2} - 45 x - 269 + 3 x - 7 = 0$

Add $- 45 x$ and $3 x$ .

$- 3 x^{2} - 42 x - 269 - 7 = 0$

Subtract $7$ from $- 269$ .

$- 3 x^{2} - 42 x - 276 = 0$

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Substitute in the values of $a$ , $b$ , and $c$ .

${(- 42)}^{2} - 4 (- 3 \cdot - 276)$

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 42$ to the power of $2$ .

$1764 - 4 (- 3 \cdot - 276)$

Multiply $- 3$ by $- 276$ .

$1764 - 4 \cdot 828$

Multiply $- 4$ by $828$ .

$1764 - 3312$

Subtract $3312$ from $1764$ .

$- 1548$